A096397 a(n) = #{ 0 <= i <= n : K(n, i) = -1 } where K(n, i) is the Kronecker symbol.

0, 0, 0, 1, 0, 2, 0, 1, 2, 0, 1, 4, 2, 6, 1, 1, 0, 8, 3, 8, 4, 6, 4, 8, 4, 0, 3, 9, 6, 14, 2, 9, 8, 10, 6, 10, 0, 18, 6, 6, 8, 20, 4, 21, 10, 12, 9, 18, 8, 0, 9, 14, 12, 26, 8, 11, 12, 18, 13, 26, 8, 30, 11, 17, 0, 24, 6, 34, 16, 22, 10, 28, 12, 36, 13, 18, 18, 30, 10, 28, 16, 0, 18, 39, 12, 32

Offset: 0

Author

Benoit Cloitre, Aug 06 2004

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000010, A051953, A096398, A071961, A372728.

Cf. A096396 (#K(n,i)=1), this sequence (#K(n,i)=-1), A062830 (#K(n,i)=0).

Programs

Maple

K := (n, k) -> NumberTheory:-KroneckerSymbol(n, k):
seq(nops(select(k -> K(n, k) = -1, [seq(0..n)])), n = 0..85);
# Peter Luschny, May 15 2024

Mathematica

Table[Count[Table[KroneckerSymbol[n, k], {k, 0, n}], -1], {n, 0, 70}]
(* Peter Luschny, May 15 2024 *)

PARI

a(n) = sum(i=0, n, if(kronecker(n, i) + 1, 0, 1))

SageMath

print([sum(kronecker(n, k) == -1 for k in range(n + 1)) for n in range(86)])
# Peter Luschny, May 16 2024

Formula

From Reinhard Zumkeller, Mar 24 2012: (Start)

a(A096398(n)) = 0;

a(n) = A000010(n) - A096396(n) for n >= 2.

a(n) = A096396(n) - A071961(n). (End)

Extensions

Offset set to 0, a(0) = 0 added, and name adapted by Peter Luschny, May 15 2024